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If A and B are two subsets of the set S, then A*B =(A\cup B) - (A\cap B) is also a set, and (A\cup B) - (A\cap B) is the subset of S shown in colour in Andrei's diagram. Hence the closure property is satisfied. |
Learn about the rules for a group and the different groups of 4 elements by doing some simple puzzles.
This article only skims the surface of Galois theory and should probably be accessible to a 17 or 18 year old school student with a strong interest in mathematics.
Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.